Topology of some special almost complex and complex manifolds

Let M be an almost complex manifold. We assume that M admits a special hermitian metric; this influences the topological structure of M. Contents: introduction; riemannian geometry and topology; holomorphic and Kaehler sectional curvatures; pinching for Kaehler manifolds; cohomology structure of a pinched Kaehler manifold; homotopy structure of a pinched Kaehler manifold; the complex projective space theorem; manifolds diffeomorphic to Psup(n)(C); existence of an almost complex structure on a special manifold. (author)